CN103869298B - A kind of distributed MIMO sky-wave OTH radar sea clutter emulation mode - Google Patents

Abstract

The invention discloses a kind of distributed MIMO sky-wave OTH radar sea clutter emulation mode, belong to radar wave communication sphere.Existing emulation mode, mainly for the sky-wave OTH radar in the single base of tradition (accurate) or bistatic ground wave radar, is not suitable for the situation of distributed MIMO sky-wave OTH radar, and the consideration of its physical factor is the most comprehensive.The present invention is directed to the situation of distributed MIMO sky-wave OTH radar, digital ray tracing is used to calculate its each transceiver channel relative to geometrical relationship between incidence and the Returning scattering direction on sea, observation area, according to this geometrical relationship, it is derived the bistatic single order of each transceiver channel and second order sea clutter normalized bi static cross section amasss expression formula；After the Doppler with transmitting-receiving propagation path transmits function phase convolution, obtain the sea clutter power spectral density of receiving terminal in conjunction with radar equation；Finally, the Random time sequence of receiving terminal sea clutter plus noise has been obtained according to this power spectral density.This emulation mode considers each factor affecting distributed MIMO sky-wave OTH radar sea clutter the most all sidedly, and precision is high, and versatility is good, has application value.

Description

A kind of distributed MIMO sky-wave OTH radar sea clutter emulation mode

One, technical field

The invention belongs to radar wave communication sphere, emulate particularly to distributed MIMO sky-wave OTH radar sea clutter Technology.

Two, background technology

The employing of distributed MIMO system is one of important trend of sky-wave OTH radar development.Sea in strong sea clutter The detection of the Ship Target of microinching is one of emphasis and difficult point of sky-wave OTH radar detection.Distributed MIMO sky wave surpasses Sighting distance radar uses the multiple cell sites and receiving station that spatial distribution is wider, and multiple cell sites launch Orthogonal injection waveform simultaneously, Arriving at target through ionospheric reflection, after the scattering of target, partial dispersion signal arrives each receiving station through ionospheric reflection, receives Standing and isolate different transmitting signal by matched filtering, last Combined Treatment completes the detection of target.Base single with traditional (accurate) Ground sky-wave OTH radar is compared, and distributed MIMO sky-wave OTH radar is relatively big due to transmitting-receiving station space interval, from different angles Degree observed object, can obtain sky and ask diversity gain；Use multiple transmitted waveform also can obtain waveform diversity gain, in anti-target The aspects such as RCS rises and falls, moving-target detection have big advantage, provide to the detection of sea microinching target in strong sea clutter New thinking.Meanwhile, the sea clutter characteristic of distributed MIMO sky-wave OTH radar is the most complicated, and different transmitting-receivings is led to Road, geometrical relationship is different, and the position at sea clutter Bragg peak is the most different；Wave path upper ionized layer state is different, miscellaneous to sea Wave modulation effect is the most different；According to frequency orthogonal transmitted waveform, frequency interval farther out time frequency also can be to sea clutter characteristic Cause and interfere significantly on.

The physical mechanism formed from sea clutter, the sea clutter analysing in depth distributed MIMO sky-wave OTH radar is special Property, set up corresponding model and it is emulated, the sea-surface target detection technique to distributed MIMO sky-wave OTH radar, The test problems solving target at a slow speed in sky-wave OTH radar strong sea clutter has great significance.

The research of Sea Clutter from HF Radar formation mechenism, can relate nineteen fifty-five D.D.Crombie the earliest for test number According to the successful explanation come by Bragg Resonance scattering mechanism radio wave Yu wave single order effect.1972, D.E.Barrick Use perturbation standard measure in border to explain the scattering mechanism of frequency electromagnetic waves on random sea, give the single order under unit are Amassing expression formula with second order sea clutter normalized bi static cross section, wherein first-order expression is applicable to single base or bistatic sky wave With the situation of ground wave radar, its second order expression is only applicable to the situation of single base ground wave radar.1999, E.W.Gill was to double The surface scattering of base frequency electromagnetic waves has carried out theory analysis, gives single order and the second order sea clutter of bistatic ground wave radar Scattering resonance state expression formula, and give on this basis in the case of given radar parameter, sea clutter plus noise time series Simulation Methods.Samuel Grosdidier etc. are for make the calculating of scattering resonance state more conform to practical situation, further Consider the characteristic of whole radar system, the factor such as including antenna radiation pattern, range attenuation, the doppler processing of reception signal, And contrast with measured data, achieve preferable effect, but its application background remains the situation of ground wave radar.At present, for The simulation study of sky-wave OTH radar sea clutter, all with (accurate) single base as application background, and for distributed MIMO sky wave For over-the-horizon radar, each transceiver channel all can regard bistatic situation as, therefore above-mentioned emulation mode is the most inapplicable.Yang Longquan Etc. analyzing the generation mechanism of First-order sea clutter, broadening principle under a day wave reflection/ground wave diffraction integrated mode, it is derived single order Sea clutter frequency displacement, broadening computing formula, the emulation to distributed MIMO sky-wave OTH radar sea clutter has certain reference Meaning.

The present invention is directed to the situation of distributed MIMO sky-wave OTH radar, use digital ray tracing to calculate it and respectively receive Send out passage relative to geometrical relationship between incidence and the Returning scattering direction on sea, observation area, according to this geometrical relationship, derive Each transceiver channel bistatic single order and second order sea clutter normalized bi static cross section amass expression formula；Many with transmitting-receiving propagation path After Pu Le transmission function phase convolution, obtain the sea clutter power spectral density of receiving terminal in conjunction with radar equation；Finally, according to this merit Rate spectrum density has obtained the Random time sequence of receiving terminal sea clutter plus noise.

Three, summary of the invention

1. to solve the technical problem that

It is an object of the invention to provide a kind of versatility good, physical factor considers more comprehensive, is applicable to distributed The emulation mode of MIMO sky-wave OTH radar sea clutter Random time sequence.Wherein to solve the technical problem that and include:

(1) each transceiver channel of distributed MIMO sky-wave OTH radar relative to the incidence on sea, observation area and returns scattered Penetrate the calculating of geometrical relationship between direction；

(2) the bistatic single order of each transceiver channel of distributed MIMO sky-wave OTH radar and second order sea clutter normalization scattering Sectional area calculates；

(3) distributed MIMO sky-wave OTH radar each transceiver channel receiving terminal sea clutter power spectral density calculates；

(4) emulation of sea clutter plus noise random event sequence.

2. technical scheme

Distributed MIMO sky-wave OTH radar sea clutter of the present invention emulates, including techniques below measure: (1) root According to transceiver channel and the geographical position in detection marine site of distributed MIMO sky-wave OTH radar, in conjunction with ionosphere state, use 3-dimensional digital ray-tracing procedure calculates the ray path between all transceiver channels and detecting location, determines relative to detection sea Plane incident electromagnetic wave and the angle of pitch of Returning scattering electromagnetic wave and azimuth；(2) according to incident electromagnetic wave and Returning scattering electricity The angle of pitch of magnetic wave and azimuth, calculate the bistatic single order of each transceiver channel and second order sea clutter normalized bi static cross section amasss, and asks With, obtain sea clutter normalized bi static cross section and amass；(3) by long-pending for the sea clutter normalized bi static cross section of each transceiver channel logical with transmitting-receiving The ionosphere doppler spread factor convolution in road, and consider the parameters in radar equation, calculate the sea of each channel reception end Clutter power spectrum density；(4) utilize the sea clutter power spectral density of each channel reception end, table look-up and obtain the noise power of this passage Level, simulation calculation obtains the sea clutter plus noise Random time sequence of each passage.

3. beneficial effect

The present invention compares background technology and has the advantage that

(1) this emulation mode is a kind of naturally expansion the to the sky-wave OTH radar sea clutter emulation of tradition (accurate) single base Exhibition, when transceiver channel location interval is less or when being zero, is the situation of tradition (accurate) list base sky-wave OTH radar.Change Yan Zhi, traditional method is the special case of this method, and therefore, by comparison, this method scope of application is wider；

(2) this emulation mode considers the geometrical relationship of transceiver channel and observation area, ionospheric channel and radar side The impact of each factor in journey, considers more comprehensive on the physical factor affecting sea clutter, and simulation accuracy is higher；

(3) this emulation mode can support the signal modeling of distributed MIMO sky-wave OTH radar and signal processing Research.

Four, accompanying drawing explanation

Figure of description is the enforcement principle flow chart of the present invention.

Five, detailed description of the invention

Below in conjunction with Figure of description, the present invention is described in further detail.With reference to Figure of description, the tool of the present invention Body embodiment divides following step:

(1) by Ionospheric Parameters, each transmitting-receiving station position of distributed MIMO sky-wave OTH radar, tranmitting frequency, see Location is put etc. in parameter input device 1 and is carried out ray tracing calculating, obtains observing the electromagnetism that on sea, each transceiver channel is corresponding Ripple is incident and the azimuth of Returning scattering and the angle of pitch；

(2) by sea parameter, and the electromagnetic wave that on device 1 calculated observation sea, each transceiver channel is corresponding enters Penetrate the azimuth with Returning scattering and the angle of pitch is input to device 2, calculate the bistatic sea clutter normalization of each transceiver channel and dissipate Penetrate sectional area, based on below equation:

σ(ω_d)=σ₁(ω_d)+σ₂(ω_d)

Wherein

${\mathrm{\σ}}_1\left({\mathrm{\ω}}_d\right)=2^4{\mathrm{\πk}}_0^2\mathrm{\Δ}{\mathrm{\ρ}}_s\underset{m=\±1}{\mathrm{\Σ}}S\left(m\stackrel{\‾}{K}\right)\frac{K^{5/2}\cos {\mathrm{\φ}}_0(\cos {\mathrm{\Δ}}_i+\cos {\mathrm{\Δ}}_s)}{2\sqrt{g}}{\mathrm{Sa}}^2\left(\frac{\mathrm{\Δ}{\mathrm{\ρ}}_s}{2}(\frac{K}{\cos {\mathrm{\φ}}_0(\cos {\mathrm{\Δ}}_i+\cos {\mathrm{\Δ}}_s)}-k_0)\right)$

${\mathrm{\σ}}_2\left({\mathrm{\ω}}_d\right){=4\mathrm{\πk}}_0^2{\left[\cos {\mathrm{\φ}}_0(\cos {\mathrm{\Δ}}_i+\cos {\mathrm{\Δ}}_s)\right]}^4\mathrm{\Δ}{\mathrm{\ρ}}_s\underset{m_1=\±1}{\mathrm{\Σ}}\underset{m_2=\±1}{\mathrm{\Σ}}{\∫}_{-\mathrm{\π}}^{\mathrm{\π}}S\left(m_1\stackrel{\‾}{K_1}\right)S\left(m_2\stackrel{\‾}{K_2}\right){\left|{\mathrm{\Γ}}_P\right|}^2\mathrm{\δ}({\mathrm{\ω}}_d+m_1\sqrt{{\mathrm{gK}}_1}+m_2\sqrt{{\mathrm{gK}}_2})K_1{\mathrm{dK}}_{1}d{\mathrm{\θ}}_{\stackrel{\‾}{K_1}}$

Represent that single order and second order sea clutter normalized bi static cross section amass respectively, in formula, ω_dRepresent Doppler frequency, Δ ρ_sTable Show the range resolution ratio of transmitted waveform, K,Being single order ocean wave number and its wave height of ocean spectrum respectively, wave height of ocean spectrum is adopted Compose with JONSWAP, φ₀Represent the half of the difference at half double-basis ditch, i.e. incident direction and Returning scattering direction azimuth, Δ_i, Δ_s Representing incident and Returning scattering direction and the angle on sea level respectively, g represents acceleration of gravity, and Sa () represents sinc function, k₀Represent and launch electromagnetism wave number, K₁,It is single order ocean wave number and its wave height of ocean spectrum, K respectively₂,Respectively It is second order ocean wave number and its wave height of ocean spectrum,It it is wave vectorDeflection；Γ_PRepresenting the coefficient of coup, it is by electromagnetism coupling Syzygy number Γ_EPWith waterpower component coefficient of coup Γ_HConstitute, i.e.

Γ_P=Γ_EP+Γ_H

${\mathrm{\Γ}}_H=\frac{1}{2}[K_1+K_2+\frac{(K_1{K}_2-\stackrel{\‾}{K_1}\·\stackrel{\‾}{K_2})}{m_1{m}_2\sqrt{K_1{K}_2}}\frac{{\mathrm{\ω}}_d^2+{\mathrm{\ω}}_B^2}{{\mathrm{\ω}}_d^2-{\mathrm{\ω}}_B^2}]$

${\mathrm{\Γ}}_{\mathrm{EP}}=\frac{1}{2}\{\frac{-(\stackrel{\‾}{K_1}\·{\widehat{\mathrm{\ρ}}}_2)[\stackrel{\‾}{K_2}\·(\stackrel{\‾}{K_1}-k_0{\widehat{\mathrm{\ρ}}}_2)]}{K\cos {\mathrm{\φ}}_0\sqrt{\stackrel{\‾}{K_1}\·(\stackrel{\‾}{K_1}-k_0{\widehat{\mathrm{\ρ}}}_2)}}+\frac{-(\stackrel{\‾}{K_2}\·{\widehat{\mathrm{\ρ}}}_1)[\stackrel{\‾}{K_1}\·(\stackrel{\‾}{K_2}-k_0{\widehat{\mathrm{\ρ}}}_1)]}{K\cos {\mathrm{\φ}}_0\sqrt{\stackrel{\‾}{K_2}\·(\stackrel{\‾}{K_2}-k_0{\widehat{\mathrm{\ρ}}}_1)}}\}$

Wherein ${\mathrm{\ω}}_B=\±\sqrt{{\mathrm{gk}}_0{\cos \mathrm{\φ}}_0({\cos \mathrm{\Δ}}_i+{\cos \mathrm{\Δ}}_s)}$ Represent single order resonance angular frequency.

(3) by calculated to the parameter of each transceiver channel, the doppler spread of transceiver path and fissipation factor and device 2 Each passage bistatic sea clutter normalized bi static cross section is long-pending is input to device 3, calculates the sea clutter power spectrum of this channel reception Degree, based on below equation:

$P_c\left({\mathrm{\ω}}_d\right)=\frac{{\mathrm{\λ}}^2{P}_t{G}_t{G}_r{\mathrm{A\σ}}_i\left({\mathrm{\ω}}_d\right)}{{\left(4\mathrm{\π}\right)}^3{\mathrm{\ρ}}_t^2{\mathrm{\ρ}}_r^2{L}_t{L}_r}$

Wherein P_tRepresent and launch power, G_tRepresent transmitter antenna gain (dBi), G_rRepresent receiving antenna gain, A=Δ R ρ_rBW_1/2Table Show that resolution cell area, Δ R represent radar range resolution, BW_1/2Represent reception antenna 3dB beam angle, ρ_tRepresent transmitter To the geometric distance in targeted propagation path, ρ_rRepresent the receiver geometric distance to targeted propagation path, L_tRepresent that transmitter is to mesh Target radio wave propagation loss, L_rRepresent the receiver radio wave propagation loss to target, σ_i(ω_d) represent by the sea behind ionosphere Clutter unit are RCS doppler spectral, its expression formula is as follows

${\mathrm{\σ}}_i\left({\mathrm{\ω}}_d\right)=\underset{m_t=1}{\overset{M_t}{\mathrm{\Σ}}}\underset{m_r=1}{\overset{M_r}{\mathrm{\Σ}}}{P}_{m_i}\left({\mathrm{\ω}}_d\right)\⊗{\mathrm{\σ}}_{m_i,m_r}\left({\mathrm{\ω}}_d\right)\⊗P_{m_r}\left({\mathrm{\ω}}_d\right)$

In formulaRepresent convolution, m_t=1,2 ..., M_t, m_r=1,2 ..., M_r, M_t, M_rRepresent respectively and launch and receive propagating mode Formula number,Represent m_iThe doppler spread factor of communication mode is penetrated in individual sending and receiving,Represent m_rIndividual reception passes Broadcast the doppler spread factor under pattern,Represent m_t-m_rThe normalization RCS doppler spectral of transceiver channel.Extend because of The calculating of son can be calculated according to the generalized power spectral function of ionospheric channel, with m_tAs a example by communication mode is penetrated in individual sending and receiving, It is represented by $P_{m_i}\left({\mathrm{\ω}}_d\right)={\mathrm{\υ}}^2+{\mathrm{\σ}}^2{\mathrm{GPSD}}_{m_i}{({\mathrm{\ω}}_{\mathrm{Dop}},\mathrm{\τ},K_x,K_y)|}_{\mathrm{\τ}=0,K_x=0,K_y=0},$ In formulaRepresent m_tIndividual The generalized power spectrum density of communication mode is penetrated in sending and receiving.

(4) the equivalent external noise factor and the sea clutter merit of the calculated each channel reception of device 3 obtained tabling look-up Rate spectrum input equipment 4, carries out Computer Simulation and i.e. obtains the sea clutter plus noise Random time sequence of each channel reception, its Process is as follows:

First, external noise power spectral density is calculated

$P_n\left({\mathrm{\ω}}_d\right)={10}^{(F_{\mathrm{am}}-204)/10}$

F in formula_amRepresent equivalence external noise factor, obtain by tabling look-up.

Secondly, for carrying a width of B, it is known that the one-dimensional stationary Gaussian process of power spectral density, its time series is

$f\left(t\right)={\∫}_B{e}^{\mathrm{j\ωt}}{e}^{\mathrm{j\ϵ}\left(\mathrm{\ω}\right)}\sqrt{F_s\left(\mathrm{\ω}\right)\frac{\mathrm{d\ω}}{2\mathrm{\π}}},$

Wherein ω ∈ [-B, B], ε (ω) are for obeying [0,2 π] equally distributed stochastic process, F_s(ω) power spectrum is represented Degree.For sea clutter F_s(ω)=P_c(ω), correspondingly, f (t)=c (t)；For noise F_s(ω)=P_n(ω), correspondingly, f (t)= n(t).Calculate for convenience of discrete values, use part and approach the integral operation of f (t), being shown below

$f\left(t\right)=\underset{({\mathrm{\ω}}_{2q+2}-{\mathrm{\ω}}_{2q})\→0}{\underset{{\mathrm{\ω}}_{2p}\→\∞}{\lim }}\underset{q=0}{\overset{p}{\mathrm{\Σ}}}{e}^{j\left({\mathrm{\ω}}_{2q+1}t\right)}{e}^{\mathrm{j\ϵ}\left({\mathrm{\ω}}_{2q+1}\right)}\·\sqrt{F_s\left({\mathrm{\ω}}_{2q+1}\right)\frac{{\mathrm{\ω}}_{2q+2}-{\mathrm{\ω}}_{2q}}{2\mathrm{\π}}}$

The power spectral density of sea clutter and noise is substituted into, i.e. can get sea clutter time series c (t) and noise temporal sequence Row n (t).

Finally, when both summations i.e. be can get driftlessness, the Random time sequence signal that each channel receiver receives

s(t)=c(t)+n(t) 。

Claims (1)

1. a distributed MIMO sky-wave OTH radar sea clutter emulation mode, it is characterised in that include techniques below measure:

(1) digital ray tracing method is used to calculate each transceiver channel of distributed MIMO sky-wave OTH radar relative to the area of observation coverage Geometrical relationship between incidence and the Returning scattering direction on sea, territory, concretely comprises the following steps: first, receives and dispatches according in each transceiver channel Standing and the position relationship of observation area, setting electromagnetic wave is from cell site to observation area, and observation area to receiving station may be passed through Ionospheric parameter and tranmitting frequency, use digital ray tracing method calculate frequency electromagnetic waves from cell site to the area of observation coverage Territory, the propagation path of observation area to receiving station；Then, obtain on sea, observation area each according to calculated propagation path The incidence of transceiver channel and the direction vector of Returning scattering；Finally, vector operation is utilized to calculate the incident and orientation of Returning scattering Angle and the angle of pitch, incident orientation angle and Returning scattering azimuth are subtracted each other and are multiplied by 0.5 both to have obtained formed horizontal plane half bistatic Angle；

(2) the normalization sea clutter radar cross section meter that each transceiver channel of distributed MIMO sky-wave OTH radar is corresponding is given Calculation formula:

σ(ω_d)=σ₁(ω_d)+σ₂(ω_d)

Wherein

${\mathrm{\σ}}_1\left({\mathrm{\ω}}_d\right)=2^4{\mathrm{\πk}}_0^2{\mathrm{\Δ\ρ}}_s\underset{n=\±1}{\Σ}S\left(m\stackrel{\→}{K}\right)\frac{K^{5/2}{\mathrm{cos\φ}}_0({\mathrm{cos\Δ}}_i+{\mathrm{cos\Δ}}_s)}{2\sqrt{g}}{\mathrm{Sa}}^2\left(\frac{{\mathrm{\Δ\ρ}}_s}{2}\right(\frac{K}{{\mathrm{cos\φ}}_0({\mathrm{cos\Δ}}_i+{\mathrm{cos\Δ}}_s)}-k_0\left)\right)$

${\mathrm{\σ}}_2\left({\mathrm{\ω}}_d\right)=4{\mathrm{\πk}}_0^2{\[{\mathrm{cos\φ}}_0({\mathrm{cos\Δ}}_1+{\mathrm{cos\Δ}}_s)\]}^4{\mathrm{\Δ\ρ}}_s\underset{m_1=\±1}{\Σ}\underset{m_2=\±1}{\Σ}{\∫}_{-\mathrm{\π}}^{\mathrm{\π}}{\∫}_{-\mathrm{\∞}}^{\mathrm{\∞}}S\left(m_1\stackrel{\→}{K_1}\right)S\left(m_2\stackrel{\→}{K_2}\right){\left|{\mathrm{\Γ}}_P\right|}^2\mathrm{\δ}({\mathrm{\ω}}_d+m_1\sqrt{{\mathrm{gK}}_1}+m_2\sqrt{{\mathrm{gK}}_2})K_d{\mathrm{dK}}_1{\mathrm{d\θ}}_{\stackrel{\→}{K_1}}$

Represent that single order and second order sea clutter normalized bi static cross section amass respectively, in formula, ω_dRepresent Doppler frequency, Δ ρ_sRepresent and send out The range resolution ratio of ejected wave shape, K,Being single order ocean wave number and its wave height of ocean spectrum respectively, wave height of ocean spectrum uses JONSWAP composes, φ₀Represent the half of the difference at half double-basis ditch, i.e. incident direction and Returning scattering direction azimuth, Δ_i, Δ_sPoint Not Biao Shi the angle on incident and Returning scattering direction and sea level, g represents acceleration of gravity, and Sa () represents sinc function, k₀ Represent and launch electromagnetism wave number, K₁,It is single order ocean wave number and its wave height of ocean spectrum, K respectively₂,It is respectively Second order ocean wave number and its wave height of ocean are composed,It it is wave vectorDeflection；Γ_PRepresenting the coefficient of coup, it is by electromagnetic coupled Coefficient Γ_EPWith waterpower component coefficient of coup Γ_HConstitute, i.e.

Γ_P=Γ_EP+Γ_H

${\mathrm{\Γ}}_H=\frac{1}{2}\[K_1+K_2+\frac{(K_1{K}_2-\stackrel{\→}{K_1}\·\stackrel{\→}{K_2})}{m_1{m}_2\sqrt{K_1{K}_2}}\frac{{\mathrm{\ω}}_d^2+{\mathrm{\ω}}_B^2}{{\mathrm{\ω}}_d^2-{\mathrm{\ω}}_B^2}\]$

${\mathrm{\Γ}}_{EP}=\frac{1}{2}\{\frac{-(\stackrel{\→}{K_1}\·{\widehat{\mathrm{\ρ}}}_2)\[\stackrel{\→}{K_2}\·(\stackrel{\→}{K_1}-k_0{\widehat{\mathrm{\ρ}}}_2)\]}{K{\mathrm{cos\φ}}_0\sqrt{\stackrel{\→}{K_1}\·(\stackrel{\→}{K_1}-k_0{\widehat{\mathrm{\ρ}}}_2)}}+\frac{-(\stackrel{\→}{K_2}\·{\widehat{\mathrm{\ρ}}}_1)\[\stackrel{\→}{K_1}\·(\stackrel{\→}{K_2}-k_0{\widehat{\mathrm{\ρ}}}_1)\]}{K{\mathrm{cos\φ}}_0\sqrt{\stackrel{\→}{K_2}\·(\stackrel{\→}{K_2}-k_0{\widehat{\mathrm{\ρ}}}_1)}}\}$

WhereinRepresent single order resonance angular frequency；

(3) method that calculating distributed MIMO sky-wave OTH radar receiving terminal sea clutter power spectral density is used considers receipts Send out passage and the doppler spread of the geometrical relationship of observation area, radar system parameters and ionospheric channel and loss factor, Distributed MIMO sky-wave OTH radar each transceiver channel receiving terminal sea clutter power spectral density computing formula is:

$P_c\left({\mathrm{\ω}}_d\right)=\frac{{\mathrm{\λ}}^2{P}_t{G}_t{G}_r{\mathrm{A\σ}}_i\left({\mathrm{\ω}}_d\right)}{{\left(4\mathrm{\π}\right)}^3{\mathrm{\ρ}}_t^2{\mathrm{\ρ}}_r^2{L}_t{L}_r}$

Wherein P_tRepresent and launch power, G_tRepresent transmitter antenna gain (dBi), G_rRepresent receiving antenna gain, A=Δ R ρ_rBW_1/2Represent and divide Distinguish that cellar area, Δ R represent radar range resolution, BW_1/2Represent reception antenna 3dB beam angle, ρ_tRepresent that cell site is to mesh The geometric distance of mark propagation path, ρ_rRepresent receiving station's geometric distance to targeted propagation path, L_tRepresent that cell site arrives target Radio wave propagation loss, L_rRepresent receiving station's radio wave propagation loss to target, σ_i(ω_d) represent by the sea clutter behind ionosphere Unit are RCS doppler spectral, its expression formula is as follows:

${\mathrm{\σ}}_i\left({\mathrm{\ω}}_d\right)=\underset{m_t=1}{\overset{M_t}{\Σ}}\underset{m_r=1}{\overset{M_r}{\Σ}}{P}_{m_t}\left({\mathrm{\ω}}_d\right)\⊗{\mathrm{\σ}}_{m_t,m_r}\left({\mathrm{\ω}}_d\right)\⊗P_{m_r}\left({\mathrm{\ω}}_d\right)$

In formulaRepresent convolution, m_t=1,2 ..., M_t, m_r=1,2 ..., M_r, M_t, M_rRepresent respectively and launch and receive communication mode Number,Represent m_tThe doppler spread factor of communication mode is penetrated in individual sending and receiving,Represent m_rIndividual reception propagating mode The doppler spread factor under formula,Represent m_t-m_rThe normalization RCS doppler spectral of transceiver channel；Spreading factor Calculating can be calculated according to the generalized power spectral function of ionospheric channel, m_tIndividual sending and receiving are penetrated communication mode and are represented byIn formulaRepresent m_tIndividual The generalized power spectrum density of communication mode is penetrated in sending and receiving.